As far as I understand if yo uwant to override templates by content type you must have a template file for each type.
In panels you can create a custom page and then create a page template file for the url of your custom page. This takes care of the PAGE display. Then, to get your individual nodes to display in this page, use a url pattern that sets the default page for all the content types you want displayed through this page as the first argument:
myhomepage.org/page-name/this-node --- with page-name being the custom page.
If you want the content types to be displayed differently you can still create node template variants for them. As long as the url string begins with the page name each of teh node variants will be rendered through the custom page.
good luck!